Data Sufficiency

If x is a positive integer, is the remainder 0 when 3^x + 1 is divided by 10?

(1) x = 4n + 2, where n is a positive integer.
(2) x > 4

To expand a bit on Statement 1:

The one's digits of powers of 3 follow the repeating sequence:
3, 9, 7, 1
3^0 ends in 1, 3^4 ends in 1, 3^8 ends in 1, etc.

So, let's look at
3^(4n+2) + 1 =
3^(4n)*3^2 + 1 =
3^(4n)*9 + 1

Now, as noted above, 3^4n always ends in 1
And when you multiply something that ends in 1 by 9, the result ends in 9

So, 3^(4n)*9 ends in 9
When we add 1, it now ends in 0
And anything that ends in 0 is evenly divisible by 10 (remainder = 0)

Here we just need to find out if X is even or odd..
For all even power of 3 the last digit is 9.

statement 1 validates this

Hi Navami,

Your statement:

For all even power of 3 the last digit is 9.

is actually not true.

3^4 = 81, which ends in a 1.
Only powers of 3 that are BOTH even AND NOT multiples of 4 will end in a 9.